A computationally efficient method for hand–eye calibration

PurposeSurgical robots with cooperative control and semiautonomous features have shown increasing clinical potential, particularly for repetitive tasks under imaging and vision guidance. Effective performance of an autonomous task requires accurate hand–eye calibration so that the transformation between the robot coordinate frame and the camera coordinates is well defined. In practice, due to changes in surgical instruments, online hand–eye calibration must be performed regularly. In order to ensure seamless execution of the surgical procedure without affecting the normal surgical workflow, it is important to derive fast and efficient hand–eye calibration methods.MethodsWe present a computationally efficient iterative method for hand–eye calibration. In this method, dual quaternion is introduced to represent the rigid transformation, and a two-step iterative method is proposed to recover the real and dual parts of the dual quaternion simultaneously, and thus the estimation of rotation and translation of the transformation.ResultsThe proposed method was applied to determine the rigid transformation between the stereo laparoscope and the robot manipulator. Promising experimental and simulation results have shown significant convergence speed improvement to 3 iterations from larger than 30 with regard to standard optimization method, which illustrates the effectiveness and efficiency of the proposed method.

[1]  Guang-Zhong Yang,et al.  Emerging Robotic Platforms for Minimally Invasive Surgery , 2013, IEEE Reviews in Biomedical Engineering.

[2]  Zijian Zhao,et al.  Hand-eye calibration using convex optimization , 2011, 2011 IEEE International Conference on Robotics and Automation.

[3]  Guang-Zhong Yang,et al.  From Passive Tool Holders to Microsurgeons: Safer, Smaller, Smarter Surgical Robots , 2014, IEEE Transactions on Biomedical Engineering.

[4]  Radu Horaud,et al.  On-line hand-eye calibration , 1999, Second International Conference on 3-D Digital Imaging and Modeling (Cat. No.PR00062).

[5]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[6]  S. Duke Herrell,et al.  Image Guidance in Robotic-Assisted Renal Surgery , 2015 .

[7]  A. Nemirovski,et al.  Interior-point methods for optimization , 2008, Acta Numerica.

[8]  Danail Stoyanov,et al.  Hand-eye calibration for robotic assisted minimally invasive surgery without a calibration object , 2016, 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[9]  Ole Ravn,et al.  Hand-Eye Calibration and Inverse Kinematics of Robot Arm Using Neural Network , 2013, RiTA.

[10]  Gerd Hirzinger,et al.  Optimal Hand-Eye Calibration , 2006, 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[11]  Yuncai Liu,et al.  A hand-eye calibration algorithm based on screw motions , 2009, Robotica.

[12]  N. Trawny,et al.  Indirect Kalman Filter for 3 D Attitude Estimation , 2005 .

[13]  Heinrich Niemann,et al.  Robust Hand-Eye Calibration of an Endoscopic Surgery Robot Using Dual Quaternions , 2003, DAGM-Symposium.

[14]  Stephen J. Wright,et al.  Numerical Optimization (Springer Series in Operations Research and Financial Engineering) , 2000 .

[15]  Jack C. K. Chou,et al.  Finding the Position and Orientation of a Sensor on a Robot Manipulator Using Quaternions , 1991, Int. J. Robotics Res..

[16]  Yiu Cheung Shiu,et al.  Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the form AX=XB , 1989, IEEE Trans. Robotics Autom..

[17]  Alexandre Krupa,et al.  Intensity-Based Ultrasound Visual Servoing: Modeling and Validation With 2-D and 3-D Probes , 2013, IEEE Transactions on Robotics.

[18]  Hui Pan,et al.  A closed-form solution to eye-to-hand calibration towards visual grasping , 2014, Ind. Robot.

[19]  Cleve B. Moler,et al.  5. Least Squares , 2004 .

[20]  Jocelyne Troccaz,et al.  Hand-eye calibration of a robot - UltraSound probe system without any 3D localizers , 2015, 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).

[21]  Alexandre Krupa,et al.  Intensity-Based Visual Servoing for Instrument and Tissue Tracking in 3D Ultrasound Volumes , 2015, IEEE Transactions on Automation Science and Engineering.

[22]  Purang Abolmaesumi,et al.  A closed-form differential formulation for ultrasound spatial calibration: multi-wedge phantom. , 2014, Ultrasound in medicine & biology.

[23]  Sébastien Ourselin,et al.  Combined 2D and 3D tracking of surgical instruments for minimally invasive and robotic-assisted surgery , 2016, International Journal of Computer Assisted Radiology and Surgery.

[24]  Tomás Pajdla,et al.  Globally optimal hand-eye calibration , 2012, 2012 IEEE Conference on Computer Vision and Pattern Recognition.

[25]  Jan Heller,et al.  Hand-eye and robot-world calibration by global polynomial optimization , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[26]  Ali Sayfy,et al.  Least Squares , 2014, Encyclopedia of Social Network Analysis and Mining.

[27]  Ben Kenwright,et al.  A Beginners Guide to Dual-Quaternions: What They Are, How They Work, and How to Use Them for 3D Character Hierarchies , 2012, WSCG 2012.

[28]  Frank Chongwoo Park,et al.  Robot sensor calibration: solving AX=XB on the Euclidean group , 1994, IEEE Trans. Robotics Autom..

[29]  Ratna Babu Chinnam,et al.  Soft Boundary Approach for Unsupervised Gesture Segmentation in Robotic-Assisted Surgery , 2017, IEEE Robotics and Automation Letters.

[30]  Allison M. Okamura,et al.  3-D Ultrasound-Guided Robotic Needle Steering in Biological Tissue , 2014, IEEE Transactions on Biomedical Engineering.

[31]  Ronghua Liang,et al.  Hand-eye calibration with a new linear decomposition algorithm , 2008 .

[32]  Garth H Ballantyne,et al.  The da Vinci telerobotic surgical system: the virtual operative field and telepresence surgery. , 2003, The Surgical clinics of North America.

[33]  Jack C. K. Chou,et al.  Eight-space quaternion approach for robotic hand-eye calibration , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

[34]  Austin Reiter,et al.  Appearance learning for 3D tracking of robotic surgical tools , 2014, Int. J. Robotics Res..

[35]  Gregory S. Chirikjian,et al.  Online ultrasound sensor calibration using gradient descent on the Euclidean Group , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[36]  Guang-Zhong Yang,et al.  Wearable Sensor Integration and Bio-motion Capture: A Practical Perspective , 2014, Body Sensor Networks.

[37]  Michael I. Miga.  Computational Modeling for Enhancing Soft Tissue Image Guided Surgery: An Application in Neurosurgery , 2015, Annals of Biomedical Engineering.

[38]  Kostas Daniilidis,et al.  Hand-Eye Calibration Using Dual Quaternions , 1999, Int. J. Robotics Res..

[39]  Xianping Huang,et al.  A flexible solution to AX=XB for robot hand-eye calibration , 2010 .

[40]  William W. Hager,et al.  A New Active Set Algorithm for Box Constrained Optimization , 2006, SIAM J. Optim..

[41]  Michal Havlena,et al.  Globally Optimal Hand-Eye Calibration Using Branch-and-Bound , 2016, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[42]  Guang-Zhong Yang,et al.  Real-time surgical tool tracking and pose estimation using a hybrid cylindrical marker , 2017, International Journal of Computer Assisted Radiology and Surgery.